Combining Multiscale Diffusion Kernels for Learning the Structural and Functional Brain Connectivity

Abstract

The activation of the brain at rest is thought to be at the core of cognitive functions. There have been many attempts at characterizing the functional connectivity at rest from the structure. Recent attempts with diffusion kernel models point to the possibility of a single diffusion kernel that can give a good estimate of the functional connectivity. But our empirical investigations revealed that the hypothesis of a single scale best-fitting kernel across subjects is not tenable. Further, our experiments demonstrate that structure-function relationship across subjects seems to obey a multi-scale diffusion phenomenon. Based on this insight, we propose a multiple diffusion kernel model (MKL) along with a learning framework for estimating the optimal model parameters. We tested our hypothesis on 124 subjects data from publicly available NKI_Rockland database. The results establish the viability of the proposed model and also demonstrate several promising features as compared to the single kernel approach. One of the key strengths of the proposed approach is that it does not require hand-tuning of model parameters but actually learns them as part of the optimization process. The learned parameters may be suitable candidates for future investigation of their role in distinguishing health and disease.